nricens: NRI for time to event models

In nricens: NRI for Risk Prediction Models with Time to Event and Binary Response Data

Description

This function estimates the NRI for competing risk prediction models with time to event variable. coxph object, survreg object, predictors, and predicted risks can be used as input data for the calculation. The risk category based NRI and the risk difference based NRI can be calculated. Users can use several types of estimators to obtain point estimates of the NRI and its components. The percentile bootstrap method is used for an interval estimation.

Usage

nricens(time = NULL, event = NULL, mdl.std = NULL, mdl.new = NULL,
        z.std = NULL, z.new = NULL, p.std = NULL, p.new = NULL, t0 = NULL,
        updown = "category", cut = NULL, point.method = "km",
        niter = 1000, alpha = 0.05, msg = TRUE)

Arguments

time	Vector of observed follow up times, X = \min(T, C). T is event time, and C is censoring time.
event	Vector of event indicators, 1 for event of interest, 0 for censoring.
mdl.std, mdl.new	coxph or survreg objects corresponding to a standard and a new risk prediction model, respectively. Since predictors are extracted from these objects, x=TRUE is required when fitting a Cox or a parametric survival model.
z.std, z.new	Matrix of predictors for a standard and a new risk prediction model, respectively. Neither factor nor character nor missing values are allowed.
p.std, p.new	Vector of predicted risks from a standard and a new prediction model, respectively.
t0	Scalar value indicating a time to determine evnet/non-event.
updown	Character to specify the method to determine UP and DOWN. When "category" is specified (by default), the risk category based NRI is calculated. When "diff" is specified, the risk difference based NRI is calculated.
cut	Scalar or vector values to specify the cutoff value(s) of predicted risks for determining UP and DOWN. For the risk category based NRI (updown = "category"), this option corresponds to cutoff value(s) of risk categories. For the risk difference based NRI (updown = "diff"), this option corresponds to a cutoff value of a risk difference (only scalar is allowed).
point.method	Character to determine an estimator for a point estimation. When "km" is specified, the Kaplan-Meier (KM) based NRI estimator is used (Pencina et al., 2011). When "ipw" is specified, the inverse probability weighting (IPW) NRI estimator is used (Uno et al., 2012).
niter	Scalar value to determine the number of bootstratp sampling. When 0 is specified, an interval estimation is skipped.
alpha	1-alpha confidence interval is calcualted.
msg	Logical value to display computation process. Setting FALSE leads silent execution.

Details

Either one set of the following arguments should be specified for the NRI calculation: (mdl.std, mdl.new); (time, event, z.std, z.new); and (time, event, p.std, p.new).

In the first set of the argument, (mdl.std, mdl.new), fitted results by coxph or survreg are used for the NRI calculation. time, event, z.std, and z.new are extracted from fitted result objects. The variance of model parameters are accounted for an interval estimation of the NRI. When time and event are specified in arguments, those specified are used without extracting from coxph or survreg objects.

In the second set of the argument, (time, event, z.std, z.new), a standard and a new prediction models are fitted inside this function with time, event, z.std and z.new. The variance of model parameters are also accounted for an interval estimation of the NRI.

In the third set of the argument, (time, event, p.std, p.new), predicted risks are used. Since fit of prediction models are not conducted while in a bootstrap, this can be used for a validation study by an external data source or by a cross-validation.

For the risk category based NRI calculation, cutoff values of risk category can be specified by cut, which is a scalar for the case of two risk categories and is a vector for the case of more than two risk categories. UP and DOWN are determined by the movement in risk categories.

For the risk difference based NRI calculation, cutoff values of risk difference can also be specified by cut, where UP and DOWN are defiend as p_{new} - p_{standard} > δ and p_{standard} - p_{new} > δ, respectively. p_{standard} and p_{new} are predicted individual risks from a standard and a new prediction model, respectively, and δ corresponds to cut. The continuous NRI, which is the special version of the risk difference based NRI, can be calculated by specifying both updown = "diff" and cut = 0.

Interval estimation is based on the percentile bootstrap method.

Value

Returns a list of the following items:

nri	Point and interval estimates of the NRI and its components.
mdl.std, mdl.new	Fitted coxph or survreg objects corresponding to a standard and a new prediction model, respectively. These items are provided when prediction models are fitted inside this function. Otherwise NULL.
z.std, z.new	Predictors of a standard and a new prediction model, respectively. These items are provided when they are extracted from mdl.std and mdl.new. Otherwise NULL.
p.std, p.new	Predicted risks by a standard and a new prediction model, respectively.
up, down	Logical values to show subjects who belong to UP and DOWN, respectively.
rtab, rtab.case, rtab.ctrl	table objects corresponding to reclassification tables for all, case, and control subjects, respectively. These items are provided only when the risk category based NRI is specified and msg = TRUE.
bootstrapsample	Results of each bootstrap sample.

References

Pencina MJ, D'Agostino RB, Steyerberg EW. Extensions of net reclassification improvement calculations to measure usefulness of new biomarkers. Statistics in Medicine 2011.

Uno H, Tian L, Cai T, Kohane IS, Wei LJ. A unified inference procedure for a class of measures to assess improvement in risk prediction systems with survival data, Statistics in Medicine 2012.

Hsu CH, Taylor JMG. A robust weighted Kaplan-Meier approach for data with dependent censoring using linear combinations of prognostic covariates, Statistics in Medicine 2010.

Examples

## here consider pbc dataset in survival package as an example
library(survival)
dat = pbc[1:312,]
dat$sex = ifelse(dat$sex=='f', 1, 0)

## predciting the event of 'death'
time  = dat$time
event = ifelse(dat$status==2, 1, 0)

## standard prediction model: age, bilirubin, and albumin
z.std = as.matrix(subset(dat, select = c(age, bili, albumin)))

## new prediction model: age, bilirubin, albumin, and protime
z.new = as.matrix(subset(dat, select = c(age, bili, albumin, protime)))

## coxph fit
mstd = coxph(Surv(time,event) ~ ., data.frame(time,event,z.std), x=TRUE)
mnew = coxph(Surv(time,event) ~ ., data.frame(time,event,z.new), x=TRUE)

## predicted risk at t0=2000
p.std = get.risk.coxph(mstd, t0=2000)
p.new = get.risk.coxph(mnew, t0=2000)

## Calculation of risk category NRI
##   by the KM estimator using ('mdl.std', 'mdl.std').
nricens(mdl.std = mstd, mdl.new = mnew, t0 = 2000, cut = c(0.2, 0.4),
        niter = 0)

##   by the KM estimator using ('time', 'event', 'z.std', 'z.std').
nricens(time = time, event = event, z.std = z.std, z.new = z.new,
        t0 = 2000, cut = c(0.2, 0.4), niter = 0)

##   by the KM estimator using ('time','event','p.std','p.std').
nricens(time = time, event = event, p.std = p.std, p.new = p.new,
        t0 = 2000, cut = c(0.2, 0.4), niter = 0)

## Calculation of risk difference NRI by the KM estimator
nricens(mdl.std = mstd, mdl.new = mnew, t0 = 2000, updown = 'diff',
        cut = 0.05, niter = 0)

## Calculation of risk difference NRI by the IPW estimator
nricens(mdl.std = mstd, mdl.new = mnew, t0 = 2000, updown = 'diff',
        cut = 0.05, point.method = 'ipw', niter = 0)

Example output

Loading required package: survival

UP and DOWN calculation:
  #of total, case, and control subjects at t0:  312 88 144

  Reclassification Table for all subjects:
        New
Standard < 0.2 < 0.4 >= 0.4
  < 0.2    139     7      1
  < 0.4     17    72      6
  >= 0.4     0     5     65

  Reclassification Table for case:
        New
Standard < 0.2 < 0.4 >= 0.4
  < 0.2      9     2      0
  < 0.4      1    21      4
  >= 0.4     0     0     51

  Reclassification Table for control:
        New
Standard < 0.2 < 0.4 >= 0.4
  < 0.2     92     4      1
  < 0.4      9    29      2
  >= 0.4     0     3      4

NRI estimation by KM estimator:

Point estimates:
                Estimate
NRI           0.11028068
NRI+          0.05123381
NRI-          0.05904686
Pr(Up|Case)   0.06348538
Pr(Down|Case) 0.01225156
Pr(Down|Ctrl) 0.09583016
Pr(Up|Ctrl)   0.03678329

STANDARD prediction model (Cox model):
               coef exp(coef)    se(coef)         z     Pr(>|z|)
age      0.03726683 1.0379699 0.009048925  4.118371 3.815600e-05
bili     0.13531179 1.1448937 0.013711323  9.868617 0.000000e+00
albumin -1.44611854 0.2354825 0.221997986 -6.514107 7.312351e-11

NEW prediction model (Cox model):
               coef exp(coef)    se(coef)         z     Pr(>|z|)
age      0.03362675 1.0341985 0.009214173  3.649460 2.627925e-04
bili     0.12517886 1.1333511 0.014406820  8.688861 0.000000e+00
albumin -1.39395237 0.2480928 0.217046959 -6.422354 1.341831e-10
protime  0.28602917 1.3311313 0.070536400  4.055058 5.012193e-05

UP and DOWN calculation:
  #of total, case, and control subjects at t0:  312 88 144

  Reclassification Table for all subjects:
        New
Standard < 0.2 < 0.4 >= 0.4
  < 0.2    139     7      1
  < 0.4     17    72      6
  >= 0.4     0     5     65

  Reclassification Table for case:
        New
Standard < 0.2 < 0.4 >= 0.4
  < 0.2      9     2      0
  < 0.4      1    21      4
  >= 0.4     0     0     51

  Reclassification Table for control:
        New
Standard < 0.2 < 0.4 >= 0.4
  < 0.2     92     4      1
  < 0.4      9    29      2
  >= 0.4     0     3      4

NRI estimation by KM estimator:

Point estimates:
                Estimate
NRI           0.11028068
NRI+          0.05123381
NRI-          0.05904686
Pr(Up|Case)   0.06348538
Pr(Down|Case) 0.01225156
Pr(Down|Ctrl) 0.09583016
Pr(Up|Ctrl)   0.03678329

UP and DOWN calculation:
  #of total, case, and control subjects at t0:  312 88 144

  Reclassification Table for all subjects:
        New
Standard < 0.2 < 0.4 >= 0.4
  < 0.2    139     7      1
  < 0.4     17    72      6
  >= 0.4     0     5     65

  Reclassification Table for case:
        New
Standard < 0.2 < 0.4 >= 0.4
  < 0.2      9     2      0
  < 0.4      1    21      4
  >= 0.4     0     0     51

  Reclassification Table for control:
        New
Standard < 0.2 < 0.4 >= 0.4
  < 0.2     92     4      1
  < 0.4      9    29      2
  >= 0.4     0     3      4

NRI estimation by KM estimator:

Point estimates:
                Estimate
NRI           0.11028068
NRI+          0.05123381
NRI-          0.05904686
Pr(Up|Case)   0.06348538
Pr(Down|Case) 0.01225156
Pr(Down|Ctrl) 0.09583016
Pr(Up|Ctrl)   0.03678329

UP and DOWN calculation:
  #of total, case, and control subjects at t0:  312 88 144
  #of subjects with 'p.new - p.std > cut' for all, case, control: 34 21 11
  #of subjects with 'p.std - p.new < cut' for all, case, control: 40 12 8

NRI estimation by KM estimator:

Point estimates:
                Estimate
NRI           0.10070960
NRI+          0.05097223
NRI-          0.04973737
Pr(Up|Case)   0.22431499
Pr(Down|Case) 0.17334277
Pr(Down|Ctrl) 0.10859064
Pr(Up|Ctrl)   0.05885327

UP and DOWN calculation:
  #of total, case, and control subjects at t0:  312 88 144
  #of subjects with 'p.new - p.std > cut' for all, case, control: 34 21 11
  #of subjects with 'p.std - p.new < cut' for all, case, control: 40 12 8

NRI estimation by IPW estimator:

Point estimates:
                 Estimate
NRI            0.06361038
NRI+           0.08444371
NRI-          -0.02083333
Pr(Up|Case)    0.22905909
Pr(Down|Case)  0.14461537
Pr(Down|Ctrl)  0.05555556
Pr(Up|Ctrl)    0.07638889

nricens documentation built on May 2, 2019, 6:01 a.m.